Explanation

(c)
Given equation can be rewritten as
$\Rightarrow \ \frac{(x - 1)^{2}}{4} + \frac{(y - 1)^{2}}{9} = 1$
Also $e = \ \sqrt{1 - \frac{4}{9}} = \frac{\sqrt{5}}{3}\ \ \lbrack\because a < b\rbrack$
$\therefore$ Equations of latusrectum are
$y - 1 = \pm 3.\frac{\sqrt{5}}{3}$ [using $y = \pm be\rbrack$
$\Rightarrow y = 1 \pm \sqrt{5}$